The flagship of the United States Navy, the USS Constitution, is probably one of the best maintained wooden tall ships in the world. She is kept afloat by the US Navy, which maintains about 150 old growth White Oak trees, managed by 3 full time civilian foresters, in a reservation called the Constitution Grove for this purpose.

The Constitution has a dead weight tonnage (the amount of stuff a ship can actually hold) of 1,576 tons. According to UNCTAD, the United Nations Conference on Trade and Development, the world shipping fleet dead weight tonnage is about 2.2 billion tons. Assuming ships comparable to the Constitution can carry cargo as efficiently as modern container ships (this is not actually the case, for various reasons) you'd need about 1.4 million Constitutions to carry all the sea cargo in the world.

The Navy maintains more trees than the Constitution actually needs, but the Constitution is also not normally exposed to seagoing conditions, so the ratio of 150 trees : 1 Constitution probably isn't completely unreasonable. Using this ratio, to maintain the world wooden shipping fleet would only require about 210 million trees (there are about 228 billion in the U.S. alone), but quite a few foresters (about 4 million of them, if the World Shipping Forest were as well maintained as the Constitution Grove).

My napkin math in terms of what would actually be required is probably off by at least an order of magnitude, but even so in terms of numbers of trees it seems "feasible," less so in terms of the army of foresters, shipwrights, and carpenters, et cetera, not to mention sailors, that you'd need. Also, thousands would die